Answer:
[tex](0.306,0.446)[/tex]
Step-by-step explanation:
The confidence interval for a population proportion is calculated using the formula;
[tex]p+/-z\sqrt{\frac{p(1-p)}{n} }[/tex]
In the above expression;
p represents the sample proportion calculated as, number of successes/sample size;
p = 120/319 = 0.3762
z represents the confidence coefficient associated with the given level of significance. In our case the confidence level required is 99%. The z-score associated with this level of significance is +/-2.576
n represents the sample size under evaluation, 319 college students.
Using the values obtained above, the 99% confidence interval for the true proportion of all college students who own a car is;
[tex]0.3762+/-2.576\sqrt{\frac{0.3762(1-0.3762)}{319} }[/tex]
[tex]0.3762+/-0.06987[/tex]
[tex](0.306,0.446)[/tex]
